Perfect state transfer on Cayley graphs over a non-abelian group of order 8n

2024/05/03 by Akash Kalita, Bikash Bhattacharjya, Kalita, Akash +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #05C25 #81P45 #81Q35 #Combinatorics (math.CO) #DNA and Biological Computing #FOS: Mathematics #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2405.02122

openalex publication_date 2024/05/03 · openalex created_date 2024/05/11 · openalex updated_date 2026/07/28

Abstract

The transition matrix of a graph Γ with adjacency matrix A is defined by H(τ) := exp(-iτA), where τ∈ ℝ and i = √(-1). The graph Γ exhibits perfect state transfer (PST) between the vertices u and v if there exists τ₀(>0)∈ ℝ such that | H(τ₀)_uv | = 1. For a positive integer n, the group V_8n is defined as V_8n := ⟨ a,b \colon a²ⁿ = b⁴ = 1, ba = a^-1b^-1, b^-1a = a^-1b ⟩. In this paper, we study the existence of perfect state transfer on Cayley graphs Cay(V_8n, S). We present some necessary and sufficient conditions for the existence of perfect state transfer on Cay(V_8n, S).

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